13 citations · 39 across the 20 of their papers we have counts for
25 papers
Singular Aubry--Mather Sets for a Homogeneous Single-Input Control System
Bernard Bonnard, Cristian Mendico
We develop an Aubry--Mather theory for the abnormal arcs of a time-minimal single-input affine control system in dimension three with homogeneous cubic drift. We show that the Bonn…
A Fully Discrete Variational Approximation of Mather Measures and Sets
Fabio Camilli, Cristian Mendico
We introduce a fully--discrete variational approximation of Mather measures and sets for Tonelli Lagrangians on the flat torus, together with a numerical procedure for approximatin…
State-Dependent Delays in Optimal Control and Hamilton--Jacobi Equations
Yiming Jiang, Cristian Mendico, Yawei Wei +2
We develop a Hamilton--Jacobi theory for finite-horizon optimal control problems governed by state-dependent delay equations. In this setting, the delayed-time map depends on the c…
Semi-Discrete Approximation of Aubry and Mather sets
Fabio Camilli, Cristian Mendico
We study the semi-discrete approximation of Aubry and Mather sets for Tonelli Lagrangians on the flat torus. Starting from the discrete Lax--Oleinik equation, we introduce natural…
Multimodal branched transport infers anatomically aligned brain reaction maps
Cristian Mendico
How external stimulation is transformed into distributed reaction patterns remains unresolved at the level of propagation architecture. Existing large-scale control models quantify…
Branched Optimal Transport for Stimulus to Reaction Brain Mapping
Cristian Mendico
A central problem in systems neuroscience is to determine how an external stimulation is propagated through the brain so as to produce a reaction. Current deterministic and stochas…
Periodic limit for non-autonomous Lagrangian systems and applications to a Kuramoto type model
Veronica Danesi, Cristian Mendico, Xuan Tao +1
This paper explores the asymptotic properties of non-autonomous Lagrangian systems, assuming that the associated Tonelli Lagrangian converges to a time-periodic function. Specifica…
Discretization and Vanishing Discount Problems for First-order Mean Field Games
Renato Iturriaga, Cristian Mendico, Kaizhi Wang +1
This article focuses two issues related to the first-order discounted mean field games system. The first is the time discretization problem. The time discretization approach enable…
Relaxed Lagrangian Approach to First-Order Non-Convex Mean Field Type Control Problem
Cristian Mendico, Kaizhi Wang, Yuchen Xu
This paper addresses the existence of equilibria for Mean Field type Control problems of first-order with non-convex action functional. Introducing a relaxed Lagrangian approach on…
Long-time behavior of generalized gradient flows of solutions to Hamilton-Jacobi equations
Paolo Albano, Piermarco Cannarsa, Wei Cheng +1
We study the long-time behavior of the generalized gradient flow associated with solutions of the critical Hamilton-Jacobi equation for mechanical Hamiltonians on the flat torus. F…
A note on first order quasi-stationary Mean Field Games
Fabio Camilli, Claudio Marchi, Cristian Mendico
Quasi-stationary Mean Field Games models consider agents who base their strategies on current information without forecasting future states. In this paper we address the first-orde…
Fokker-Planck equations on homogeneous Lie groups and probabilistic counterparts
Lucia Caramellino, Cristian Mendico
We address the well-posedness of subelliptic Fokker-Planck equations arising from stochastic control problems, as well as the properties of the associated diffusion processes. Here…
Rate of convergence for first-order singular perturbation problems: Hamilton-Jacobi-Isaacs equations and mean field games of acceleration
Piermarco Cannarsa, Cristian Mendico
This work focuses on the rate of convergence for singular perturbation problems for first-order Hamilton-Jacobi equations. As an application we derive the rate of convergence for s…
Semi-linear parabolic equations on homogeneous Lie groups arising from mean field games
Paola Mannucci, Claudio Marchi, Cristian Mendico
The existence and the uniqueness of solutions to some semilinear parabolic equations on homogeneous Lie groups, namely, the Fokker-Planck equation and the Hamilton-Jacobi equation,…
Quantitative and qualitative properties for Hamilton-Jacobi PDEs via the nonlinear adjoint method
Fabio Camilli, Alessandro Goffi, Cristian Mendico
We provide some new integral estimates for solutions to Hamilton-Jacobi equations and we discuss several consequences, ranging from -rates of convergence for the vanishing vis…
Analysis of the vanishing discount limit for optimal control problems in continuous and discrete time
Piermarco Cannarsa, Stephane Gaubert, Cristian Mendico +1
A classical problem in ergodic continuous time control consists of studying the limit behavior of the optimal value of a discounted cost functional with infinite horizon as the dis…
Aubry-Mather theory for optimal control systems with nonholonomic constraints
Piermarco Cannarsa, Cristian Mendico
In this work, we extend Aubry-Mather theory to the case of control systems with nonholonomic constraints. In this framework, we consider an optimal control problem where admissible…
Differential N-players game: Nash equilibria and Mather measures
Cristian Mendico
We study Nash equilibria for the deterministic ergodic N-players game. We introduce pure strategies, mixed strategies and Nash equilibria associated with those. We show that a Nash…
Aubry set for sub-Riemannian control systems
Piermarco Cannarsa, Cristian Mendico
In the paper [P. Cannarsa, C. Mendico, Asymptotic analysis for Hamilton-Jacobi- Bellman equations on Euclidean space, (2021) Arxiv], we proved the existence of the limit as the tim…
A singular perturbation problem for mean field games of acceleration: application to mean field games of control
Cristian Mendico
We study the singular perturbation problem for mean field game systems with control of acceleration. For such a problem we analyze the behavior of solutions as the acceleration cos…
Asymptotic analysis for Hamilton-Jacobi-Bellman equations on Euclidean space
Piermarco Cannarsa, Cristian Mendico
The long-time average behavior of the value function in the calculus of variations is known to be connected to the existence of the limit of the corresponding Abel means. Still in…
Ergodic behavior of control and mean field games problems depending on acceleration
Pierre Cardaliaguet, Cristian Mendico
The goal of this paper is to study the long time behavior of solutions of the first-order mean field game (MFG) systems with a control on the acceleration. The main issue for this…
Weak KAM approach to first-order Mean Field Games with state constraints
Piermarco Cannarsa, Wei Cheng, Cristian Mendico +1
We study the asymptotic behavior of solutions to the constrained MFG system as the time horizon goes to infinity. For this purpose, we analyze first Hamilton-Jacobi equations w…
Mild and weak solutions of Mean Field Games problem for linear control systems
Piermarco Cannarsa, Cristian Mendico
The aim of this paper is to study first order Mean field games subject to a linear controlled dynamics on . For this kind of problems, we define Nash equilibria (cal…